Consider the system X'(t) = | x(t),t > 0. If the eigenvalues of the coefficient matrix are r= -1 and r=-3, then the general solution of the given system is -3t -3t a) X(t) = c1 + c2 b) X(t) = c1 -t e -3t c) X(t) = c1 G) -t e + C2 et d) X(t) = c1 + C2 3t

Consider the system X'(t) = | x(t),t > 0. If the eigenvalues of the coefficient matrix are r= -1 and r=-3, then the general solution of the given system is -3t -3t a) X(t) = c1 + c2 b) X(t) = c1 -t e -3t c) X(t) = c1 G) -t e + C2 et d) X(t) = c1 + C2 3t

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Consider the linear system 2 A₁ = Find the eigenvalues and eigenvectors for the coefficient matrix.…

Q: Q2: (a) For given matrix A, find a 3 x 3 non-singular matrix P such that p-1AP is diagonal. A = |-3…

Q: The coefficient matrix A of the 4x4 system below has eigenvalues A₁ = -6, A₂= -3, A-6, and A4 =11.…

A: Given information:The system of differential equation is that:Eigenvalues are given as .Initial…

Q: d) If the equations have infinite number of solutions, determine the value of k e) Suppose *₂ = t…

Q: | 50 9

Q: 2 = 1+ 2i [1 -1] X' = 4 1

Q: The coefficient matrix A of the 4 x 4 system below has eigenvalues A₁-7. g=-4, Ag 9, and 14. Find…

Q: The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the…

Q: [1 0 [9 0 01 c) A-2 = |0 4 0 Lo o 1l 9. Find a matrix A that satisfies a) (3.4) =0 -1 1 |0 0 -1| 2.

A: ANSWER :

Q: 3. (a) Diagonalize the matrix 4-(-3). A = i.e. write A = VAV-1, where V is the matrix whose colums…

A: From the given information:

Q: Q1: Solve the linear system using Crammer rule: 2x + y + 2z = 4 x – 2y + 3z = 9 y - z = -3

A: As per the company policy i can answer only first question for you,more than that leads me towards…

Q: 1. (a) Construct a 3 x 3 matrix A such that the solution set of the equation Ax = 0 is the line in…

Q: that|k= te soluti 15 kx tyt y + ky kydy

A: Given system is,kx+y+kz= k2x+ky+z=kkx+y-kz=k2 If k=0, prove that the system has infinite number of…

Q: (a) Oë + pà + pax = (b) # + mx(1 – ±²)+ vg(x) = Asparagus(t), x(1) = -5, ±(1) = 10…

A: This is a problem of IVP.

Q: A=18, B=22 Give a 2x2 matrix that will project any point (x, y) on to the line going through (0, 0)…

Q: O A₁2, V₁ = = O A₁2, V₁ = = O A₁-2, V₁ = = The phase portrait shown above is for a linear system…

Q: 6. (a) Find the determinant of the inatrix B = 1 -2 0 0 3 1 1 2 4 -1 -1 1 -4 (b) Solve the system Bx…

Q: Xn+1 = TXn, here %D T = [ Find the eigenvalues and the corresponding eigenvectors. Write the form of…

Q: C = Problem 8. If a ‡ 0, 1 and A = ( ¦ ¦ ), B = ( 8 5), Find AT (B+C), b) Find (aA + B)-¹, c) Find…

Q: -3 [73] 4 -2 Av= -3x + 3y or 4x - 2y✔ o 4(A3) = (| –12x+12yv ở, 16x−8y, ở Let A = Enter the…

Q: Find a fundamental matrix for the system = (; 3)* -2' x'(t) : 2 -2

A: x't=3-22-2x Let A=3-22-2 Characteristic equation of A is given by λ2-trAλ+detA=0 where trA is the…

Q: Consider matrices A E F"," , b E F",. Select all true statements about system of linear equations Ax…

A: Let A∈Fn,n,b∈Fn,1 and the system of linear equation is Ax=b The given statements are: 1. If the…

Q: (c) Consider the quadratic form f(x1, x2, x3) = 3(a₁x₁ + a2x2 + a3x3)² = 4(b₁x₁ + b₂x2 + b3x3)². (i)…

Q: (b) Consider a linear system Ax = b with A = 2 -1 0 -1 3 -1 0-1 4 and b = ( −7, 6, 17 )T. (i) Prove…

A: We have system AX=b A=[2-10-13-10-14], X= [xyz], b=[-7617]

Q: solve this plz

Q: ii) Find the particular solution showing the amount of deer at a particular time given that 100 deer…

A: Your (ii) and (iii) problem can't be solved because not enough information is given

Q: 6. (a) Find the determinant of the matrix B = -2 0 1 1 -1 0 2 1 3 4 (b) Solve the system Bx = 0,…

A: Here for given 4 x 4 matrix we have to find the determinant of the matrix B. And find the solution…

Q: (a) Consider the system of equations 11х3 — Зх1 yi %3D - 7x1 – 6x2 – 5x3 y2 х> + 2х3 — 2х = y3…

Q: The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the…

A: We have to find the general solution of the given system of differential equations.

Q: -3 *-[1]-*-[;)] and Az = 2a - 4b. = Let A be a 3 x 2 matrix with linearly independent columns.…

A: x is just the linear combination of u and v.

Q: Let A be an invertible matrix such that A-¹ = 2 2 01 1 1 0 -1 3 0] Solve the system (4A²)x = b,…

Q: 2. (a) Find the condition number of the coefficient matrix in the system (1761) (22) = (2²6) as a…

Q: The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply eigenvalue…

Q: 8. The Cramer's Rule fails to apply to a linear system Ax = b, where A is a square matrix, if (a)…

A: Solution: Given data, In Cramers rule we have to find the determinent and it is divided with 1.

Q: For a linear DDS with multiple equations, assume that A is the matrix of the system with eigenvalue…

Q: Let A be a 2 x 2 diagonalizable matrix. 3et+ ecit If is the solution to the system ở' (t) = Ax(t),…

Q: Find the 3x3 homogeneous matrix for 2D-reflection across a line that goes through (B, C) and makes…

A: As per the question we have to to find the transformation matrix which reflects any point on 2d…

Question

Consider the system X'(t) = X(t), t > 0. If the eigenvalues of the
coefficient matrix are r= -1 and r= -3, then the general solution of the given
system is
a) X(t) = C1
+ C2
-3t
e
e
b) X(t) = c1 (;) e-t + c2
-3t
e
c) X(t) = c1
(다)
,-t
е
+ C2
e-t
d) X(t) = c1
et
3t
C2

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Matrix Eigenvalues and Eigenvectors$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the eigenvalue method to find a general solution of the system. x₁ = 3x₁ + x2 + x3, x2 = -7x₁5x2-X3, X3 = 7x₁ + 7x2 + 3x3 What is the general solution in matrix form? x(t) =
Find the LU factorization of A = and then use it to solve the system -4 -3 3 16 15 -11 A = x1 = x₂ = x3 = 8 -6 -8 || x1 x2 x3 = -4 -3 3 16 15 -11 8 -6 -8 -31 127 44 " such that the matrix L has ones along the diagonal,
A system of ordinary differential equations has 2 x 2 state matrix with eigenvalues and corresponding eigenvectors (eigenpairs) A1 = 5, v1 = and A2 = -6, Based on the given eigenpairs write down the general solution to the associated system of differential equations. The solution must be written as a |¤1(t) single vector like a =
The coefficient matrix A of the 4x4 system below has eigenvalues A₁-9, A₂-6, Ag 9, and 4 14. Find the particular solution of this system that satisfies the initial conditions x₁ (0) = 5, x₂ (0) = 5, x₁ (0) = 5, x4 (0) = 5. x₁ = 2x₁ + x₂ + xy + 8x4 x2 = x₁ + 2x₂ + 11xg+X4 X3 X₁ +11x₂ + 2xy +Xg x48x₁ + x₂ + xy + 2x₁ *(t) =
-2 Q2: A) If A' = and the det = -2 -1/2] find the matrix A and what is the rank of this matrix ? B) Solvė the following matrix equations for x,y and z x 3 - y [3 71 - XJ
(a) Use Gauss-Jordan elimination to find the inverse of the given matrix A 1 1 3 3 -1 1 A = -1 -3 -4 2 -5 2 (b) Given b = (1.1.2.2) solve the system by suing x = A-'b.
In this problem you will solve the nonhomogeneous system 2 1 -e -2 0 -4e t A. Write a fundamental matrix for the associated homogeneous system B. Compute the inverse -5 -1 C. Multiply by gand integrate -2e^(-t) -3e^(-t) (Do not include c and cz in your answers). D. Give the solution to the system [8 Ci+ (Do not include c¡ and c2 in your answers).
8. Solve the linear system Ax-b by x₁ + x₂-3x₂ = -1 -x₁ + 2x₂ = 1 x₁ - x₂ + x₂ = 2 a) finding the LU-factorization of the coefficient matrix A b) Solving the lower triangular system Ly-b. c) solving the upper triangular system Ux-y.
Suppose the eigenvalues associated with a 2 by 2 matrix of a system of linear ODE's are complex conjugates. (a) Use Euler's formula to rewrite the solution in the form x(t) = u(t) + iv(t). (b) Show that x(t) = u(t) + v(t) is also a solution of the system.